Dipole-lets: a new multiscale decomposition for MR phase and quantitative susceptibility mapping
Nondipolar phase contributions can generate severe streaking artifacts during quantitative susceptibility mapping (QSM) inversion. We propose Dipole-lets, a dipole-adapted multiscale decomposition designed to identify phase components associated with streaking artifacts before and during susceptibility inversion. Dipole- lets combine an undecimated radial decomposition with an angular partition based on proximity to the magic cone. The resulting coefficients emphasize phase components near the magic cone, where nondipolar contributions may become relatively prominent. This information was incorporated into QSM reconstruction through a data- driven fidelity weight and a Dipole-let-based regularizer that models an additional nondipolar phase component. The methods were evaluated using modified simulated QSM data and an in vivo dataset. The data-driven weighting reduced streaking artifacts while preserving anatomical detail and improved quantitative reconstruction metrics compared with magnitude-weighted TV. The Dipole-let regularizer achieved streaking suppression comparable to L1-QSM and lower reconstruction error in the modified simulated dataset. In vivo experiments further demonstrated the applicability of the proposed approach to data with strong susceptibility-induced phase perturbations. Dipole-lets provide a multiscale representation for characterizing phase components associated with streaking artifacts and incorporating this information into QSM reconstruction, reducing streaking while preserving relevant susceptibility structures, and providing a flexible basis for future QSM reconstruction methods.